1. Field of the Invention
The present invention relates to a resin-made non-spherical optical element, an optical scanning device using the optical element, and an image forming apparatus using the optical scanning device.
2. Discussion of the Background
Optical elements such as plastic lenses formed by plastic molding of a resin material are widely used for reducing weight and cost of an optical system or for shaping a surface of the optical elements in a special shape.
A shape of a coaxial non-spherical surface (a non-spherical shape having a rotational symmetry with respect to an optical axis), which is typical as a special surface shape, is generally expressed by the following formula (1) using: a distance in the direction orthogonal to an optical axis, r; a depth in the optical axis direction, f(r); a radius of curvature on the optical axis, R; and constant numbers, K, A1, A2, A3, . . . ,
f(r)=(r2/R)/[1+{(1xe2x88x92(1+K)(r/R)2}]+A1r+A2r2+A3r3+A4r4+A5r5+A6r6+xe2x80x83xe2x80x83(1)
As the number of terms of higher degree on the right side of equation (1) increases, the shape of the non-spherical surface becomes more complicated, so that correction of wave-front aberration can be more finely made.
A complicated shape of a non-spherical surface can be formed in a precise manner by plastic molding. However, as known, in plastic molding a surface sink mark and an internal distortion tend to occur in the periphery of a molded piece.
Accordingly, in plastic molding, anticipating that a surface sink mark and/or an internal distortion occur in the periphery of a molded piece, it is necessary to prevent the surface sink mark and/or the internal distortion from extending toward an effective area (e.g., in a lens, an area within an effective lens diameter in which the design optical function can be assured) of the molded piece.
Therefore, for example, when manufacturing a lens having a non-spherical surface by plastic molding, a sufficient margin is provided to the outside of the effective diameter of the lens, i.e., the outside of the effective area of the lens, so that even if a surface sink mark or an internal distortion occurs at the periphery of the margin, the effective area is not affected by such a surface sink mark or an internal distortion.
As the degree of a term of higher degree of (r) on the right side of the above formula (1) is higher, when a lens is relatively large, a change in the depth in the axial direction of the lens is excessively large at the periphery of the lens, so that a difference in the thickness of the lens greatly differs between the vicinity of the optical axis and the periphery of the lens. In this case, when making a metal mold for plastic molding, due to constraint of a contact angle between a tip end of a cutting bite and a surface of the metal mold and of a resolution of bite moving steps, a desired surface shape cannot be obtained in the metal mold. As a result, a sufficient margin cannot be obtained at the outside of an effective area of the lens surface, thereby causing a surface sink mark and/or an internal distortion in the plastic molding.
Further, because a time period for cooling differs between the center part and the peripheral part of the lens because of the above-described relatively large thickness difference, the above-described surface sink mark and/or internal distortion tend to occur often.
Furthermore, depending upon the non-spherical shape, when (r) is relatively large, it may occur that {(1xe2x88x92(1+K)(r/R)2} on the right side of the above formula (1) is negative and {(1xe2x88x92(1+K)(r/R)2} is an imaginary number, such that the non-spherical surface itself cannot be expressed. In this case also, a sufficient margin cannot be obtained outside of the effective area of an optical surface.
For example, a lens constituting an fxcex8 lens as a scanning image forming lens system of an optical scanning device may be relatively large such that the lens diameter in the main scanning direction exceeds 200 mm. In such a case, the above-described problem tends to occur rather often.
As a method for avoiding the above-described problem, in optical designing, a design may be made for a range broader than an effective area that is actually needed. However, the optimum optical performance may be shifted toward an outside of an effective diameter of a light ray, and as a result, the optical performance in the effective area may deteriorate.
Further, a straight line part (i.e. a flat part) that is discontinuous from a shape of an effective area may arise outside of the effective area. In this case, however, because a boundary between the effective area and an area outside of the effective area is discontinuous, in molding, the surface accuracy deteriorates in the vicinity of the boundary.
The present invention has been made in view of the above-discussed and other problems and addresses the above-discussed and other problems.
Preferred embodiments of the present invention provide a novel resin-made non-spherical optical element in which a relatively large area is provided outside of an effective area on its optical surface having a non-spherical shape so that an adverse affect of a surface sink mark and/or an interior distortion will not extend to the effective area.
Further, the preferred embodiments of the present invention provide an optical scanning device capable of performing a satisfactory optical scanning by using such a resin-made non-spherical optical element, and an image forming apparatus capable of performing a satisfactory image formation by using the optical scanning device.
A resin-made non-spherical optical element according to an embodiment of the present invention is a resin-made optical element made by plastic molding, in which at least one optical surface is formed in a non-spherical shape. The optical surface of the optical element having the non-spherical shape includes an effective area and an area located outside of the effective area.
Here, the non-spherical shape can include not only a coaxial non-spherical shape but also a non-arc shape in which the shape in the main scanning cross-section and/or the shape in the sub-scanning cross-section are non-arc. Further, the non-spherical shape includes a sub-scanning non-arc shape in which the non-arc shape in the sub-scanning cross-section changes in the main scanning direction. For example, a cylindrical surface and a toric surface have non-spherical shapes.
The optical surface here means a surface formed substantially in a mirror-surface-like surface by a metal mold with plastic molding. Rib parts and gate parts are excluded from the optical surface.
The effective area here is an area on an optical surface where the optical performance of the optical surface is assured. For example, in a lens for condensing a deflected light flux onto a scanned surface in optical scanning, the effective area is a combined area of an area where a light flux scanning the optical surface for forming an image on the scanned surface passes, an area where a light flux for synchronization detection passes, and an area into which a light flux may be shifted due to tolerances of the parts.
Thus, because the effective area of an optical surface is an area where an optical performance of the optical surface is assured, surface accuracy, internal distortion, and alien substances in the effective area must be managed so that the optical performance is assured in the effective area.
The area outside of the effective area is an area outside of the effective area on the above-described optical surface. The optical surface shape in the area outside of the effective area is set to smoothly continue to the optical surface shape in the effective area, and is formed in a shape different from the non-spherical shape in the effective area. Accordingly, in the area outside of the effective area, the above-described optical performance is not assured. When the above-described {(1xe2x88x92(1+K)(r/R)2} is an imaginary number so that a non-spherical shape cannot be expressed, a shape different from the non-spherical shape in the effective area refers to a concrete shape replacing the non-spherical shape.
The shape of the optical surface having the non-spherical shape in the area outside of the effective area can be a shape obtained by multiplying a shape of the optical surface in the area outside of the effective area, that is extended from the non-spherical shape in the effective area, by a damping function so that a change in an optical axis direction in the shape of the optical surface in the area outside of the effective area is damped.
For example, when a coordinate in the main scanning direction is expressed by Y, a coordinate in the sub-scanning direction is expressed by Z, a non-spherical shape expressing an optical surface is expressed by X(Y,Z), and a shape of the non-spherical shape X(Y,Z) in the effective area is expressed by Xin(Y,Z) and a shape thereof in the area outside of the effective area is expressed by Xout(Y,Z), if the coordinate position Y, Z is within the effective area, then X(Y,Z)=Xin(Y,Z) holds, and if the coordinate position Y, Z is out of the effective area, then X(Y,Z)=Xout(Y,Z) holds.
At this time, in an actual shape of the optical surface, by multiplying the shape in the area outside of the effective area Xout(Y,Z) by a damping function, a change in the shape in the area outside of the effective area is damped. For example, the shape of the optical surface in the area outside of the effective area can be made as expressed by the following formula:
Xout(Y,Z)=X(Y,Z){1+(Hxe2x88x92H0)xc3x97Damp}.
In this formula, H0 is a distance of a position of the border between the effective area and the area outside of the effective area from an optical axis of an optical element, and H is a distance of a position in the area outside of the effective area from the optical axis. Damp is a factor suppressing a change in a shape. Damp can be a constant number, or can be made as follows as a function of Hxe2x80x2=Hxe2x88x92H0:
Damp(Hxe2x80x2)=D0+D1Hxe2x80x2+D2Hxe2x80x22+D3Hxe2x80x23 . . .
In the above formula, {1+(Hxe2x88x92H0)xc3x97Damp} is a damping function.
The above-described resin-made non-spherical optical element can be configured such that the optical surface having the non-spherical shape has shapes different from each other in two directions that are orthogonal to an optical axis and to each other. In this case, the optical surface in at least one of the two directions is an anamorphic optical surface having a non-arc shape, and the optical surface includes the effective area and the area outside of the effective area in the direction in which the optical surface has the non-arc shape. This optical element can be a lens for use in an optical scanning device in which the two directions orthogonal to each other correspond to a main scanning direction and a sub-scanning direction. Further, the optical element can be used in a scanning image forming optical system of the optical scanning device, which condenses a light flux deflected by a deflector toward a scanned surface to be formed into an optical spot on the scanned surface.
In the above-described optical element, the shape of the optical surface having the non-spherical surface in the area outside of the effective area can be made into a shape having a slope expressed by a 1st derivative at an outermost periphery of the effective area in the non-spherical shape.
When a non-spherical shape in the effective area is expressed by Xin(Y,Z), a shape of the area outside of the effective area is expressed by Xout(Y,Z), a coordinate of a border between the effective area and the area outside of the effective area is expressed by H0 with the optical axis position as the origin of coordinates, and a coordinate in the area outside of the effective area is expressed by H with the optical axis position as the origin of coordinates, a shape of the area outside of the effective area is expressed by the following formulae:
xe2x80x83Xout(Y,Z)=[Xin(H0,Z)]+{∂[Xin(Hc,Z)]/∂Y}xc3x97(Hxe2x88x92Hc) with respect to the main scanning direction; and
Xout(Y,Z)=[Xin(Y,H0)]+{∂[Xin(Y,Hc)]/∂Z}xc3x97(Hxe2x88x92Hc) with respect to the sub-scanning direction.
Here, ∂[Xin(Hc,Z)]/∂Y and ∂[Xin(Y,Hc)]/∂Z are inclination coefficients (1st derivatives) of the area outside of the effective area at H0.
With the above-described configuration, a shape sharply inclined in the area outside of the effective area can be made to be moderately inclined.
The above-described optical element may be configured such that the optical surface having the non-spherical shape has shapes different from each other in two directions that are orthogonal to an optical axis and to each other. In this case, the optical surface in at least one of the two directions is an anamorphic optical surface having a non-arc shape, and the optical surface includes the effective area and the area outside of the effective area in the direction in which the optical surface has the non-arc shape.
Further, the above-described optical element may be a lens for use in an optical scanning device in which the two directions orthogonal to each other correspond to a main scanning direction and a sub-scanning direction. In this case, the optical element can be used in a line image forming optical system of the optical scanning device, which forms a light flux coupled from a light source side into a line image extending in the main scanning direction in a vicinity of a deflecting reflective surface of a deflector.
Each of the above-described resin-made non-spherical optical elements may be configured to satisfy a condition We/Wo less than 0.9 (2), in which the width of an optical surface is Wo and the width of the effective area is We.
In making a resin-made non-spherical optical element by plastic molding, a satisfactory surface can be obtained over a large area of an optical surface of the optical element by making a molding tact time longer. However, considering mass production efficiency, for avoiding a surface sink mark and/or an interior distortion from adversely influencing an effective area of the optical surface, it is effective to make an area outside of the effective area relatively large.
Therefore, by making an effective area smaller than 90% of an optical surface as in the above condition We/Wo less than 0.9 (2), a satisfactory optical element can be obtained. That is, after setting the size of an effective area of an optical surface to a necessary size, according to the set size of the effective area, the width of the optical surface can be determined so as to satisfy the condition We/Wo less than 0.9 (2).
An optical scanning device for optically scanning a scanned surface according to an embodiment of the present invention includes a light source, a coupling lens to couple a light flux from the light source to a subsequent optical system, a deflector to deflect the coupled light flux, and a scanning image forming optical system to condense the deflected light flux toward the scanned surface to be formed into an optical spot on the scanned surface so that the scanned surface is scanned by the optical spot. A resin-made non-spherical optical element of the present invention is arranged on an optical path from the light source to the scanned surface.
The optical scanning device may further include a line image forming optical system that forms a light flux coupled from a light source side into a line image extending in the main scanning direction in the vicinity of a deflecting reflective surface of a deflector. In this case, resin-made non-spherical optical elements of the present invention may be used in the line image forming optical system and in the image forming optical system. Further, a resin-made non-spherical optical element of the present invention may be used as a mirror.
An image forming apparatus according to an embodiment of the present invention includes a photosensitive medium and an optical scanning device of the present invention for scanning the photosensitive medium to form an image thereupon.
Various known types of photosensitive media can be used in the image forming apparatus. For example, a photographic printing paper that is colored by heating may be used for the photosensitive medium. An image can be formed by optically scanning the photographic printing paper with an optical spot and by thereby coloring the photographic printing paper by heat energy of the optical spot.
A photosensitive medium on which a latent image is formed by optical scanning may also be used. The latent image is made visible and thereby an image is formed. Further, a silver film may be used for the photosensitive medium. A latent image formed on a silver film by optical scanning is developed and fixed according to a known process for the silver film. Image forming apparatuses using such a photosensitive medium can be practiced as an optical plate making apparatus and an optical drawing apparatus.
Furthermore, a photoconductor may be used for the photosensitive medium. In this case, an electrostatic latent image is formed, which is then made visible as a toner image. The toner image is finally transferred onto a sheet-like-shaped recording medium.
A known zinc oxide photosensitive paper may also be used as the photoconductor. In this case, a toner image formed on the zinc oxide photosensitive paper is fixed on the zinc oxide photosensitive paper serving as a sheet-like-shaped recording medium.
When a photoconductor that can be repeatedly used is used, a toner image formed on the photoconductor is transferred onto a transfer sheet or an OHP sheet (a plastic sheet for use with an overhead projector) directly or via an intermediate transfer medium such as an intermediate transfer belt. The transferred toner image is fixed onto the transfer sheet or OHP sheet, and thereby a desired image is obtained.
The above-described image forming apparatus can be practiced as a digital copying machine, an optical printer, a facsimile machine, etc. Further, because image formation is performed by optical scanning, image information input to an optical scanning device of the image forming apparatus may be obtained by optically reading an original manuscript, generated by a computer, transmitted from an external source, etc.